Damage inspection and health monitoring of dynamical systems by advanced time-frequency analysis

Abstract

This paper presents a conjugate-pair decomposition (CPD) method for offline damage inspection and online health monitoring of dynamical systems. Responses of damaged dynamical systems are often nonlinear and nonstationary. For a nonlinear non-stationary signal, empirical mode decomposition (EMD) uses the apparent time scales revealed by the signal's local maxima and minima to sequentially sift intrinsic mode functions (IMFs) of different time-varying scales, starting from high- to low-frequency ones. For offline detailed damage inspection, CPD uses one or more pairs of windowed adaptive harmonics and function orthogonality to track time-varying frequency and amplitude of each IMF. Because CPD processes only time-domain data, it is free from the edge effect caused by Gibbs' phenomenon and other mathematical and numerical problems caused by the use of Hilbert transform. Hence, results from CPD are valuable for accurate identification of dynamical systems. For parametric identification, one can compare the time-varying frequency and amplitude from CPD with those from perturbation analysis to determine the type and order of nonlinearity and system parameters. For online health monitoring, CPD tracks the instantaneous frequency of an arbitrary signal without signal decomposition by processing three or more most recent data to estimate its instantaneous frequency and amplitude. Numerical results show that CPD is versatile for system identification, damage inspection, and health monitoring of different linear/nonlinear dynamical systems.